Home
Class 12
MATHS
If f(x) is a function satifying f(1/x) +...

If `f(x)` is a function satifying `f(1/x) + x^(2)f(x) = 0` for all non-zero x, then `int_(sintheta)^("cosec" theta)f(x) dx` is equals to :

A

`sintheta+cosestheta`

B

`sin^(2)theta`

C

`cosec^(2)theta`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - II|23 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 2 Part - III|30 Videos

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE|Exercise Exercise 1 Part-III|2 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

  • DPP

    RESONANCE|Exercise QUESTION|665 Videos

Similar Questions

Explore conceptually related problems

If f(x) is a function satisfying f(1/x)+x^(2)f(x)=0 for all non zero x then int_(cos theta)^(sec theta)f(x)dx=

If f(x) rArr int_(sin theta)^("cosec" theta) f(x)dx equals

If f(x) is a function satisfying f((1)/(x))+x^(2)f(x)=0 for all nonzero x, then evaluate int_(sin theta)f(x)dx

If f(x) and g(x) are continuous functions satisfying f(x) = f(a-x) and g(x) + g(a-x) = 2 , then what is int_(0)^(a) f(x) g(x)dx equal to ?

If f(x) is a continuous function satisfying f(x)=f(2-x) , then the value of the integral I=int_(-3)^(3)f(1+x)ln ((2+x)/(2-x))dx is equal to

If 2f(x) - 3 f(1//x) = x," then " int_(1)^(2) f(x) dx is equal to

If a continuous function f satisfies int_(0)^(f(x))t^(3)dt=x^(2)(1+x) for all x>=0 then f(2)

Let f(x) be a function defined on R satisfying f(x)=f(1x) for all x in R. Then int_(-(1)/(2))^((1)/(2))f(x+(1)/(2))sin xdx equals

RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - 1
  1. Let A = int(0)^(1)(e^(t))/(1+t) dt, then int(a-1)^(a)(e^(-1))/(t-a-1) ...

    Text Solution

    |

  2. int1^2 x^(2x^2+1)(1+2lnx)dx is equal to

    Text Solution

    |

  3. If f(x) is a function satifying f(1/x) + x^(2)f(x) = 0 for all non-ze...

    Text Solution

    |

  4. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

    Text Solution

    |

  5. If f(x) = int(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt, f(x+pi) is equal to :

    Text Solution

    |

  6. Let f(x) = int(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x) be the inverse of ...

    Text Solution

    |

  7. Let f(x) is differentiable function satisfying 2int(1)^(2)f(tx) dt ...

    Text Solution

    |

  8. Let I(n) = int(0)^(1)x^(n)(tan^(1)x)dx, n in N, then

    Text Solution

    |

  9. If u(n) = int(0)^(pi//2) x^(n)sinxdx, then the value of u(10) + 90 u(...

    Text Solution

    |

  10. The value of int(1//e)^(tanx)(t)/(1+t^(2))dt+int(1//e)^(cotx)(1)/(t(1+...

    Text Solution

    |

  11. Let A(1) = int(0)^(x)(int(0)^(u)f(t)dt) dt and A(2) = int(0)^(x)f(u).(...

    Text Solution

    |

  12. lim(nrarroo) (sin'(pi)/(2n).sin'(2pi)/(2n).sin'(3pi)/(2n)"......."sin'...

    Text Solution

    |

  13. Area bounded by the region consisting of points (x,y) satisfying y le ...

    Text Solution

    |

  14. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

    Text Solution

    |

  15. The area bounded by the curve x = a cos^3t,, y = a sin^3t, is :

    Text Solution

    |

  16. The area bounded by the curve f(x)=x+sinx and its inverse function bet...

    Text Solution

    |

  17. P(2,2), Q(-2,2) R(-2,-2) & S(2,-2) are vertices of a square. A para...

    Text Solution

    |

  18. The ratio in which the curve y = x^(2) divides the region bounded by ...

    Text Solution

    |

  19. If f(x)=sinx ,AAx in [0,pi/2],f(x)+f(pi-x)=2,AAx in (pi/2,pi)a n df(x)...

    Text Solution

    |

  20. The area bounded by the curves y = x e^(x), = x e^(-x) and the line ...

    Text Solution

    |